## Convection

Convection dominates in the lower parts of the martian atmosphere. Heat is transferred between regions of different temperature through movement of the material. Convection occurs when a parcel of air in a planet' s atmosphere is slightly warmer than its surroundings. The parcel expands in an attempt to re-establish pressure equilibrium. However, this expansion causes the parcel's density to decrease below that of the surroundings. The parcel then rises as it seeks a region with equivalent density. But the pressure of the surroundings decreases with height, causing the rising parcel to expand as it rises. The parcel's temperature drops as it expands. The temperature of the surroundings also decreases with height above the surface. If the temperature of the surroundings decreases sufficiently rapidly with height, the parcel remains warmer than its surroundings. Thus, the parcel continues to rise and transports heat upward. Alternately, cold air is denser than its surroundings and will descend. Atmospheres where energy transport is dominated by convection have a temperature structure which follows an adiabatic lapse rate. No heat is exchanged between the convecting parcel and the surroundings under adiabatic conditions.

The temperature structure of an atmosphere undergoing convection can be derived from the equation of hydrostatic equilibrium (Eq. 6.2) and basic thermo-dynamic relations. Conservation of energy within the atmosphere is obtained from the first law of thermodynamics:

The amount of heat absorbed from the surroundings by a system is dQ. This is related to the change in internal energy of the system (dU) and the work done by the system on its environment (PdV, where P = pressure and dV = change in volume). The thermal heat capacities of the atmosphere at constant volume (CV) and constant pressure (CP) are given by

The specific volume (V) is the volume per unit mass. Density (q) is related to specific volume through

Differentiating the ideal gas law (Eq. 6.3) and substituting Eq. (6.12) for the density, we find